Elusive physical electron propagator in QED-like effective theories

TL;DR

This paper investigates the form of the physical electron propagator in QED-like models relevant to high-temperature superconductors, finding that the conjectured gauge-invariant form has a negative anomalous dimension and proposing a super-Luttinger decay instead.

Contribution

It demonstrates that the previously conjectured gauge-invariant electron propagator is not suitable and introduces the idea of a super-Luttinger decay behavior in these theories.

Findings

The stringy ansatz is the only gauge-invariant candidate.

The ansatz has a negative anomalous dimension.

The physical electron may exhibit super-Luttinger decay.

Abstract

We study the previously conjectured form of the physical electron propagator and its allegedly Luttinger type of behavior in the theory of the pseudogap phase of high-temperature copper-oxide superconductors and other effective QED-like models. We demonstrate that, among a whole family of seemingly gauge-invariant functions, the conjectured "stringy ansatz" for the electron propagator is the only one that is truly invariant. However, contrary to the results of the earlier works, it appears to have a negative anomalous dimension, which makes it a rather poor candidate to the role of the physical electron propagator. Instead, we argue that the latter may, in fact, feature a "super-Luttinger" behavior characterized by a faster than any power-law decay: G(x) ~ exp(-const ln^2|x|).